While, as discussed above, we are mainly interested in edge-centric measures, and more specifically in Ricci curvature, one can also define the Forman-scalar curvature, in manner similar to the \(PL\)  manifolds case pioneered by Stone [1]} (see also [2]}), to be
\(\kappa _{{\bf F}(v)} = {\bf F}(v)= \sum _{e_k \sim v} {\rm Ric}_F(e_k)\,;\) 
